Finite-state discrete-time channels with equiprobable M-ary inputs are considered. The generating function bound, which is ubiquitously applied to upper-bound the error probability of uncoded signaling over these channels, is used here to lower-bound the corresponding generalized symmetric cutoff rate, which lower-bounds the practically achievable rates and error exponents in these channels with symmetric signaling. The bound accounts for general additive metrics. For the special case of the optimal maximum-likelihood metric, the corresponding bound is shown to be asymptotically tight in the region where the symmetric cutoff rate approaches its maximum value of log/sub 2/ M (bits-per-channel use). For a finite-state additive white Gaussian noise (AWGN) channel this feature is used to relate the minimum Euclidean distance of an uncoded symmetric system to the corresponding symmetric cutoff rate. The results are demonstrated for AWGN channels corrupted by linear and nonlinear intersymbol interference. They are also used to assess the efficiency of concatenated coding over the 4-ary AWGN channel where the finite-state mechanism is defined by simple rate 1/2, four-state Ungerboeck 4-AM trellis code.>

For transmitting compressed digital video, the authors propose using threshold decodable block codes with large block length, and a posteriori probability (APP) soft decision decoding. A new approximation of the weight function associated with APP soft decision decoding of threshold decodable codes is presented. When the number of components in the parity equations is large, the new method gives excellent error performance, whereas there is a substantial degradation in the performance of the least reliable symbol approximation presented by Tanaka et al. (1980) and others. The effect of feedback on the performance of the APP decoder is also analyzed. It is shown that if the performance criterion is word error rate rather than bit error rate, feedback of previously decoded bits is essential to obtain all possible coding gain from the soft decision decoder. Finally, the performance of the proposed coding scheme is compared to the performance of a concatenated coding system with the same rate.>

Two different methods of soft-decision demodulation for channels with finite intersymbol interference (ISI) in the presence of additive white Gaussian noise (AWGN) are analyzed. In both schemes, the cutoff rate R/sub 0/ of the discrete channel created by the demodulator output quantization is chosen as the design criterion. Expressions for the optimal thresholds of the quantizer associated with the demodulation of binary signals are derived. Results for the channel with memory equal to one symbol duration are presented. As a special case, the (1-D) channel with soft decision demodulation is analyzed. Closed-form solutions show that a 4-b quantizer improves performance substantially in this case.>

A systematic way to design nonuniformly spaced tapped-delay-line (TDL) equalizers is described, and the performance of such equalizers is compared to that of uniformly spaced TDL equalizers with the same number of tap coefficients. It is shown that the signal-to-mean-squared-error ratio at the output of a TDL equalizer can be improved by optimally choosing the positions of the tap weights. An algorithm to find both the tap positions and the corresponding tap weights for a given delay span and a given minimum tap spacing of the equalizer is presented. Typical results are illustrated by using, as an example, the magnetic recording channel. For two target waveforms at different densities of recording, it is shown that there is a potential for saving up to seven equalizer taps.>

The performance of finite intersymbol interference (ISI) channels in the presence of additive white Gaussian noise is evaluated by interpreting the ISI channel as a trellis code. Closed form results are obtained for ISI channels with one and two symbols of interference. An efficient algorithm is also introduced to evaluate the minimum free Euclidean distance of any ISI channel.>

The cutoff rate of a discrete memoryless channel whose output sequences are from a (d, k) encoder is investigated. A rational rate (d, k) encoder is considered as a finite state machine and maximum-likelihood decoding is used to compute the cutoff rate. Some commonly used (d, k) codes, such as the rate 1/2 (1, 3) code with a two-state encoder, the IBM rate 2/3 (1, 7) code having a five-state encoder, and the IBM rate 1/2 (2, 7) code with a seven-state encoder, are used to illustrate the cutoff rate computation. Results are presented for both the binary symmetric channel (BSC) and the Gaussian noise channel. The performance of a decoder designed for noiseless transmission of (1, 3) code is compared to that of a maximum-likelihood decoder for the (1, 3) code. It is also shown that for the case of the Gaussian noise channel, a gain of about 1.7 dB in signal-to-noise ratio is possible by using 3-bit soft decisions over hard decisions.>